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Laws of Motion — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsLaws of Motion3 Marks
Question
In the system of three blocks $A , B$ and C shown in figure,
(i) how large a force $F$ is needed to give the blocks an acceleration of $3 m / s ^2$, if the coefficient of friction between blocks and table is $0.27$
(ii) how large a force does the block $A$ exert on the block $B$ ?
✓

Answer

Irt a be the acceleration of the system to right. All the three frictional forces $f_1 = \mu \text{m}_1\text{g}, f_2 = \mu \text{m}_2\text{g} \text{ and }f_3 = \mu \text{m}_3\text{g}$ will be directed to the left as the motion of bodies is to the right.
Hence, for the whole system

​​​​​​​ $\text{F} - \mu \text{m}_1\text{g} - \mu \text{m}_2\text{g} - \mu \text{m}_3\text{g} = (\text{m}_1 + \text{m}_2 + \text{m}_3) \text{a}$
$\text{F} = (\text{m}_1 + \text{m}_2 + \text{m}_3) (\text{a} + \mu \text{g}) $
$= (7.5 + 2 + 1)(3 + 0.2 \times 9.8) = 22.3N $
The force exerted by the 1.5kg block on the 2kg block = $\text{F} - \text{m}_1(\text{a} + \mu \text{g})$
$= 22.3 - 1.5 (3 + 0.2 \times 9.8) = 22.3 - 7.44 = 14N$

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